Can someone take a look at my system? Suggestions?

No, you won't have a problem.  Go for it.

The BIC is a powered sub with its own amp and has nothing to do with the Kenwood. You should be fine!

Ok thanks, researched as much as i could before asking, only left me more confused.

The Altecs are probably the only things you should keep.  Which ones do you have?   Why do you think the Altecs need replacement as opposed to anything else in your system?

Try it and see.  It will work.

If it does not sound good enough,  then go from there.

There are always ways to make things sound better when needed.

I remember the vintage Kenwoods well.   Very nice for the day!   However most receivers are not capable of getting the best sound quality possible out of many modern design speakers, which these days  tend to go for extended bass in a smaller package,  and are harder to drive optimally, which could make a receiver like that the bottleneck.

The advertised frequency response for those little guys  to 46 hz along with associated low 85 db sensitivity, plus  4ohm nominal impedance tells me the Kenwood may do Ok but  you could probably do much better with a modern high quality higher power amp with greater current delivery capabilty.

Specifications

Speaker type: 3-way, bass reflex
Tweeter: 1 x 1-inch soft dome, concentrically mounted
Midrange: 1 x 4-inch aluminum cone
Woofer: 1 x 5.25-inch aluminum cone
Crossover frequency: 270 / 2,700 Hz
Frequency response: 46 to 25,000 Hz
Sensitivity: 85 dB at 2.83 v/1m
Recommended amplifier power: 40 to 140 wpc
Peak power handling: 140 wpc
Nominal impedance: 4 Ω; minimum 3.4 Ω
Binding posts: 5-way custom
Magnetic shielding: No
Cabinet finishes: Black brushed vinyl
Accessories included: Magnetic fabric grille
Height: 12.75 in / 324 mm
Width: 7.87 in / 200 mm
Depth: 10.75 in / 273 mm

Chayro, there labeled “atlantic”. They sound ok but was hoping to get a better sound with some modern speakers. As far as the rest of the system. I picked up the kenwood amp, receiver, tape deck along with a technics sl d2 for $120. These were all in origional boxes and in like new condition. Im happy with the setup, just looking to improve.

Im open to suggestions on a modern integratted amp.  I really like the sound of the phono stage of this kenwood though.

That Kenwood amp is an excellent amplifier.  I owned one back in the 70's and drove a pair of Rectilinear 3 speakers with it.  Try it, you will be pleasantly surprised.