1) Can I / would it be possible for me to draw on my home's equity so that I can invest more in the market?
Yes, of course. You could get a HELOC or a cash-out refinance or buy on a margin call.
2) What factors should I consider before attempting this if it is possible?
For example, how do I determine whether it will be more profitable to do this rather than keep things as they are?
There are two parts to this kind of planning.
a) What do you want to achieve and how will you try to achieve it?
b) What could go horribly wrong, how could I avoid or minimize it, and can I live with it?
So, part (a):
Historical US stock market return has been about 10% with historical average inflation being about 3%, for a 7% real return.
Those are average returns. Any given year could be wildly better or worse than that average.
Margin call seems simple. You buy more stock than the money you have to invest with because the brokerage loans you the money. I have no idea what the fees or interest rates are for this. I understand that if the market drops "enough" the brokerage will contact you and expect you to pony up whatever cash amount it takes to restore your credit with them. I'm not sure what the penalty is if you can't do that but I expect it's not pleasant. Back in 1929 some folks in that position killed themselves.
It's not worth the hassle to solidly learn how to do this right for "play money" investment levels and no way in hell would I accept that much risk with a big chunk of my portfolio. Your mileage may vary.
So, let's try a heloc or cash-out refinance.
Let's pretend your cost to borrow that money is 4%. You're making the difference -- again on average.
One risk is that *some* HELOCs have a call option, in which the bank can say, "Um, things are tough for us right now so pony up the entire HELOC balance right away or we take your home." Again, no way would I accept that level of risk. Other HELOCs don't have that call option. I'm unaware of any cash-out refinance that has a call option. Either way, you should ALWAYS ask ahead of time and ALSO READ THE WHOLE DAMN LOAN DOCUMENT just to be sure. Sometimes the bastards lie or sometimes they're just clueless.
If your interest rate is fixed, then as inflation happens your repayment amount gets relatively cheaper (assuming your income keeps up with inflation). If the interest rate isn't fixed, then you have to understand how high it could go and what that would do to your payment and your returns.
What could go wrong? If you lose your job you could have to sell those stocks to continue to make payments. You might lose your job because the economy just tanked and stocks sell at 1/2 price. In that case, for as long as you have to do that, you're losing money. If it's a long recession and it takes you a long time to get another job, you could be losing money for a couple of years or more.
Hope that helps.
Personally, it's not something I would do. But others have made a fair bit of money doing it. And others have lost their fortunes and house.